标题： 超越系综：婴儿宇宙、时空虫洞以及黑洞信息的有序与无序 显示英文标题

标题： Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information

摘要： 在20世纪80年代，Coleman的工作以及Giddings和Strominger的工作将时空虫洞的物理与“婴儿宇宙”和一组理论的集合联系起来。 我们重新审视这些观点，利用负宇宙常数和渐近AdS边界相关的特性来加强结果，引入视角的变化，并与近期关于Page曲线的副本虫洞讨论相联系。 一个关键的新特点是强调了零模态的作用。 我们在简单的内部拓扑模型中详细探讨了这一结构，这些模型允许我们计算相关边界理论的完整谱。 渐近AdS希尔伯特空间的维度实际上成为了一个随机变量$Z$，其值可能小于理论中独立状态的朴素数量$k$。 对于$k>Z$，一致性来自于由引力路径积分定义的内积中的精确简并，因此许多原本独立的状态仅通过一个零模态有所不同。 我们认为，在任何一致的引力路径积分中都必须存在类似性质。 我们还评论了向更复杂模型外推的其他方面，以及对上述集合中个体成员的黑洞信息问题的可能影响。 显示英文摘要

摘要： In the 1980's, work by Coleman and by Giddings and Strominger linked the physics of spacetime wormholes to `baby universes' and an ensemble of theories. We revisit such ideas, using features associated with a negative cosmological constant and asymptotically AdS boundaries to strengthen the results, introduce a change in perspective, and connect with recent replica wormhole discussions of the Page curve. A key new feature is an emphasis on the role of null states. We explore this structure in detail in simple topological models of the bulk that allow us to compute the full spectrum of associated boundary theories. The dimension of the asymptotically AdS Hilbert space turns out to become a random variable $Z$, whose value can be less than the naive number $k$ of independent states in the theory. For $k>Z$, consistency arises from an exact degeneracy in the inner product defined by the gravitational path integral, so that many a priori independent states differ only by a null state. We argue that a similar property must hold in any consistent gravitational path integral. We also comment on other aspects of extrapolations to more complicated models, and on possible implications for the black hole information problem in the individual members of the above ensemble.